What is the Fermi energy of (undoped) graphene?

In summary, the Fermi energy of graphene has been measured using a double-layer heterostructure. It can also be calculated from known quantities such as the Fermi velocity, though the usual formula may not work in all cases. The Fermi energy for undoped graphene is equal to the energy at the Dirac points, which is always greater than zero.
  • #1
Izzhov
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All of the sources I have found for this online have been wildly unclear. Many use the phrase "Fermi energy" to refer to the "Fermi level" (which is emphatically not what I'm looking for; I want the Fermi energy as defined in this Wikipedia article: http://en.wikipedia.org/wiki/Fermi_energy ). Fermi energy is always greater than zero.

Has anyone ever measured the Fermi energy of graphene? Is there any way to calculate it from known quantities, such as the Fermi velocity, which is approx. [itex]10^6[/itex] m/s? i.e. is there a reason why the usual formula [itex]E_F = \tfrac{1}{2}m_e v_F^2[/itex] wouldn't work here? I read that the Fermi energy for undoped graphene is equal to the energy at the Dirac points, but I read elsewhere that that value is less than zero, which makes no sense because, again, Fermi energy is always greater than zero.
 
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  • #3
Izzhov said:
All of the sources I have found for this online have been wildly unclear. Many use the phrase "Fermi energy" to refer to the "Fermi level" (which is emphatically not what I'm looking for; I want the Fermi energy as defined in this Wikipedia article: http://en.wikipedia.org/wiki/Fermi_energy ). Fermi energy is always greater than zero.

I think ,though many use the phrase "Fermi energy", they should know their "Fermi energy" just as the "Fermi level" in their mind. Even though wikipedia have already provided "a few key differences between the Fermi level and Fermi energy", we still need to consider them carefully for our specific system. Here,consider a simplest system (just,say,hydroden atom),we use a universal DFT tool (for example, Vasp.5.2)to examine the "Fermi level". The related energy results are as follows (which are extracted from OUTCAR):

Free energy of the ion-electron system (eV)
---------------------------------------------------
alpha Z PSCENC = 0.00238712
Ewald energy TEWEN = -2.04282400
-1/2 Hartree DENC = -5.62336435
-exchange EXHF = 0.00000000
-V(xc)+E(xc) XCENC = 1.90272023
PAW double counting = 0.87256925 -0.87765194
entropy T*S EENTRO = -0.02820948
eigenvalues EBANDS = -6.30934890
atomic energy EATOM = 12.07484263
---------------------------------------------------
free energy TOTEN = -0.02887945 eV

energy without entropy = -0.00066997 energy(sigma->0) = -0.01477471

-------------------------------------------------------------------------------------

average (electrostatic) potential at core
the test charge radii are 0.5201
(the norm of the test charge is 1.0002)
1 -41.6613


E-fermi : -6.3093 XC(G=0): -0.4452 alpha+bet : -0.0289
add alpha+bet to get absolut eigen values

k-point 1 : 0.0000 0.0000 0.0000
band No. band energies occupation
1 -6.3093 1.00000
2 -0.1793 0.00000
3 0.8620 0.00000
4 0.8620 0.00000
5 0.8620 0.00000
6 1.2780 0.00000
----------------------------------------------------------------------------------------​

Where,"E-fermi:-6.3093" is just the "Fermi level".Because here is only one electron in "Hydroden atom" system, the "Fermi level" is also equal to the "eigenvalues EBANDS",but,it is not equal to the total energy as wikipedia said.
On the other hand, "Fermi energy" (not the real meaning of many people) can't be seen directly from the results above,because it is included in the total energy.
From the view of classical theory,we may understand them easier. (see that:
http://guide.ceit.metu.edu.tr/thinkquest/apndx3.htm)
 

What is the Fermi energy of (undoped) graphene?

The Fermi energy of undoped graphene is a measure of the highest energy state that can be occupied by an electron at absolute zero temperature. It is a constant value for a specific material and is often used to describe the electronic properties of materials.

Is the Fermi energy of (undoped) graphene the same as the Fermi level?

No, the Fermi energy and Fermi level are not the same. The Fermi level is the energy level at which there is a 50% probability of finding an electron, whereas the Fermi energy is the maximum energy that an electron can have at absolute zero temperature.

How is the Fermi energy of (undoped) graphene calculated?

The Fermi energy of undoped graphene can be calculated using the formula EF = h2/2m, where h is Planck's constant and m is the effective mass of the electron in graphene.

What is the significance of the Fermi energy in graphene research?

The Fermi energy is an important parameter in graphene research as it helps in understanding the electronic properties of the material. It also plays a crucial role in determining the behavior of electrons in graphene, such as their mobility and conductivity.

Can the Fermi energy of (undoped) graphene be changed?

Yes, the Fermi energy of graphene can be changed by doping the material with different impurities or by applying external electric fields. This can alter the number of electrons or holes in the material, thus affecting the Fermi energy.

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